To eradicate something is to get rid of it so completely that it is gone — pulled out by the root, which is what the Latin pieces say. We use it for big, serious targets: a disease, a pest, a cruel practice, sometimes poverty in a slogan. You would not eradicate a stain on a shirt or eradicate your homework; that is too heavy a word. Doctors talk about eradicating a disease when they mean wiping it out, not just bringing the numbers down. With social problems, people promise to eradicate them, though actually that is a very high bar, and the word can sound like a politician’s promise. If you only cut the top off a weed, it comes back; eradicate means you took the root.